Let us now discuss our merger rate formula following Refs. [1]}, [2]}., we insert a factor \((1+z)^{\alpha _z}\) , where \(\alpha _z\)  is a positive index, as an Ansatz to parametrize our ignorance about clustering dynamics. Typical values of the index \(\alpha _z\)  include \(\alpha _z=0\) , i.e. a constant merger rate, as assumed in Refs. [3]}, [4]}, [5]} or \(\alpha _z=1.3\)  as in Refs. [6]}, [7]}
